Writing Exponential Functions to Solve Problems

Objective

Students will be able to write exponential functions and equations to solve problems more efficiently. Students will be able to solve these equations using data tables, guess-and-check or other methods.

Big Idea

Develop an efficient algorithm for solving exponential word problems using ideas that actually make sense!

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Precalculus and Calculus

Standards

Warm-Up

30 minutes

Applications of Exponential Functions Warm-up 3.docx

Investigation and New Learning

45 minutes

Exponential Growth and Decay.docx

Half Life Exceeds Problem Set.docx

Find the Rate of Growth or Decay.docx

Sharing and Closing

10 minutes

I ask all students to think about these questions, and to write their initial thoughts.

The questions are deliberately open-ended and broad so that all students can answer the same questions, even though they have been working on different problems. The goal for all students is to explain how to use exponential functions to solve the problems they were working on. The challenge for most students will be to explain how this process is different depending upon the different information that is given. Students may struggle to articulate this, so this is a good example of a time to focus on MP6, and ask students to explain their thinking as precisely as possible.

Additionally, the closing asks students to assess their level of understanding. Hopefully, students will identify that they don't really have a good way to "work backwards" with these exponential functions. If some students bring up logarithms, that is great, but don't tell them that they are right. Ask them why they think logarithms might apply, or how to use them. The goal of the closing is to surface some of these questions. This is one important aspect of MP1, for students to identify their strengths and weaknesses.